Evaluation of Structural Behavior of Externally Prestressed Segmented Bridge with Shear Key under Torsion

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1 [ 鍵入文字 ] Journal of Engineering, Project, and Production Management 2011, 1(1), Evaluation of Structural Behavior of Externally Prestressed Segmented Bridge with Shear Key under Torsion M. A. Algorafi 1, A. A. A. Ali 2, I. Othman 3, M. S. Jaafar 2, and R. A. Almansob 4 1 Department of Civil Engineering, Sana a University, Sana a, Yemen, gorafimg@gmail.com (corresponding author). 2 Department of Civil Engineering, Universiti Putra Malaysia, Serdang, Selangor, Malaysia. 3 Department of Civil Engineering, University of Malaya, Kuala Lumpur, Malaysia. 4 Department of Civil Engineering, Universiti Kebangsaan Malaysia, 43600, Bangi Selangor, Malaysia. Engineering Management Received April 15, 2011; received revision May 23, 2011; accepted June 5, 2011 Available online June 20, 2011 Abstract: Externally Prestressed Segmented (EPS) concrete beams are generally used in the construction of bridge structures. External Prestressed technique uses tendons that are placed completely outside the concrete section and attached to the concrete at anchorages and deviators only. Segmented bridge is a bridge built in short sections. Segmented bridge applies smart technique that is a part of an engineering management. EPS bridges are affected by combined stresses i.e., bending, shear, normal, and torsion stresses especially at the segments interface joints. Previous studies on EPS bridges did not include the effect of torsion in the load carrying capacity and other structural behavior. This paper presents an experimental investigation of the structural behavior of EPS bridged under combined bending, shear, normal, and torsion stresses. The aim of this paper is to improve the existing equation to include the effect of torsion in estimating the failure load of EPS bridge. A parametric study was carried out to investigate the effect of different external tendon layouts and different levels of torsion. Keywords: Combined load, externally prestressed, segmented concrete bridge, torsion. 1. Introduction Externally Prestressed Segmented (EPS) concrete box bridges have been successfully designed and used in structures all over the world. Un-bonded external prestressing tendons are used for many types of construction. The technique is also a useful for the rehabilitation and strengthening of existing structures. The construction of segmented bridges with un-bonded tendons offers some advantages such as substantial economical savings due to the possibility of weatherindependent segment production, shorter construction period, simple element assembly at job site, replaceability of tendons and optimal corrosion protection of the prestressing tendons and improved fatigue behaviour. The analysis of a concrete member with an un-bonded external tendon is complicated because of the fact that strain compatibility of concrete and prestressing tendon at a section can no longer be applied. If friction is ignored, the force in the tendon is constant between the anchorages under all loads. When the tendon is external, there is an additional difficulty due to the change in tendon eccentricity with applied loads. This change in eccentricity should be accounted for by considering the equilibrium of the structure at its deformed position. Since friction occurs only at deviators, the loss of tendon force due to friction is smaller compared to that in the internal tendons. When the applied load increases, the external tendon slips at deviators resulting in redistribution of the tendon force, which affects the displacements of the member. Furthermore, the analysis of externally prestressed structure should also account for the cases where the tendon is bonded or un-bounded at the deviators. This is because, in the case where the external tendon is bonded at deviators, the force in the tendon is constant only between deviators whereas when the tendon is un-bonded (assuming no friction or free slip) the force in the tendon is constant along the entire length of the tendon between anchorages. When a structure is constructed with precast segments assembled with external prestressing, the possible opening of the joints between the segments at high applied load should be considered in the analysis. Since internal reinforcements do not cross the joints, only external prestressing should carry the additional tension due to increase in loads. Thus, the force in the tendon is dependent on the magnitude of the joint opening.

2 Evaluation of Structural Behavior of Externally Prestressed Segmented Bridge with Shear Key under Torsion Previous Studies Many investigations on segmental structures with external prestressing were carried out in the last few decades, but most of them were restricted to a load combination of bending and shear such as in the research carried out by Below et al. (1975), Misic et al. (1978), and Rabbat and Solat (1987). Ramos and Aparicio (1996) and Turmo et al. (2005) developed a finite element method for the ultimate analysis of externally prestressed bridge (monolithic and segmental). The method evaluates the behavior of internal force and prestressing tendon under combined bending moment and shear. Three types of elements were generally considered to represent the concrete beam, the tendon and the joint in segmental construction. The representation included the material and geometry nonlinearities. The aim of the study was to obtain accurate values of stress increase of the tendons beyond the effective prestress, thus ignoring the effect of friction. A good correlation has been found between the results of the study and previous test results. Aparicio et al. (2002) presented the results of a test program on external prestressed concrete beams. Five monolithic and three segmental beams were tested in bending and in combined bending and shear. The ultimate load capacity of external prestressed beams has a significant influence on the tendon length as well as shear behavior of open joints. The comparison between the test results and those predicted by the numerical model gave differences lower than 15%. Turmo et al. (2006) discussed a study on the performance of concrete segmental bridges with shear keys focusing on the shear behavior of castellated dry joints under ultimate limit state conditions. The formula used to evaluate joint shear strength was compiled. The results obtained in these tests were compared with several design formulae for assessing the load-carrying capacity of dry interlocked joints without epoxy, identifying the formula that gave the best predictions. Only a few investigations dealt with the influence of a combined loading of bending, shear, and torsion on the behavior of segmental structures such as by Kordina et al. (1984) and Falkner et al (1997). Huang et al. (2006) presented an analytical model to investigate the behavior of a prestressed segmental bridge with unbounded tendons under combined loading of torsion, bending, and shear. A modified skew bending model was developed to calculate the load-carrying capacity of segmental bridges subjected to combined forces. It was concluded that the ultimate bending and shear strength of monolithic and segmental girders were virtually the same. Only the torsional capacity of the segmental box girder was reduced. Algorafi et al. (2007) presented a detailed review of the behavior of prestressed bridges under combined stresses with a particular emphasis on external prestressed segmental bridge beams. The study concluded that a comprehensive analytical and experimental research on SEP bridges and found that the bridges were under stresses resulting from combined bending, shear, normal and torsion forces. Algorafi et al. (2010) and Algorafi (2011) presented a series of tests that were conducted to study the effect of torsion, joint type and tendon layout on the behavior of external prestressed segmental concrete box beams. The beams behavior was evaluated in terms of vertical deformation, twist angle, segment opening, tendon strain, load capacity and failure mode. The studies found that the structural behavior of EPS beams was significantly affected by torsion. A number of researches had investigated the characteristics of external prestressed segmented beams under shear force or combination of bending and shear. However, there is insufficient research work on the characteristics of external prestressed segmented box bridge under combined bending moment, shear force, normal force and torsion including the effect of various parameters such as tendon layout and joint types. The currently used AASHTO design equation does not consider the effect of combined bending moment, shear force, normal force and torsion to estimate the EPS beam failure load capacity. Therefore, there is a need for more research work to investigate the behavior of externally prestressed segmented box bridge under this combined loading which includes torsion. In this paper, the research of Algorafi et al. (2010) is extended to develop a new equation to evaluate the capacity of segment joint under combined loading (bending moment, shear force and torsion). It depended on the results of experiments of Algorafi et al. (2010) to improve the existing equation to evaluate the capacity of EPS bridge under combined loading. 3. Method 3.1. Experimental Program To investigate the effect of torsion, two series of EPS beams (with different tendon layouts) under three vertical load cases (different load eccentricities) were tested. Details of the 6 beams are shown in Table 1. Each beam had three segments (two symmetrical edge segments and one middle segment) as shown in Fig. 1. The dimensions and reinforcement details are shown in Fig. 2. Double 7 wire of 0.5 inch diameter strand with external prestressing tendons (ASTM A Grade 270) were used which were made in contact with the beam at anchorages and deviator only (Fig. 1). The area of each tendon was 98.7 mm2 (Algorafi et al. 2010). The effect of the different parameters were studied to investigate the load at onset point of nonlinearity, joint opening load, failure load, twist angle and failure mechanism of EPS bridges. The parameters are: tendon layout (straight and harp) and the level of torsion (applied by providing eccentricity of 0 mm, 100 mm and 200 mm) Test Setup and Instrumentation The assembly of each beam was first done by arranging the segments close together on temporary supports. After that the two prestressed tendons were laid through the anchorages and deviator. Two thick steel plates (600mm X 600mm X 20mm) were placed at the end of the edge segments. The steel plates were used to ensure a uniform distribution of prestress forces on the beams. Each beam was loaded with three point load with 2.4m span length as shown in Fig. 3. The prestress load was applied using a 30 kn capacity jack at each tendon. The vertical load was applied using a 500 kn jack capacity as shown in Fig. 3. The supporting arrangement at the bottom of the beam was designed to simulate hinge support by using two solid steel shaft of 50 mm diameter. However, both ends of the

3 30 M. A. Algorafi, A. A. A. Ali, I. Othman, M. S. Jaafar, and R. A. Almansob beam were fixed against rotation about beam axis using the frame as shown in Fig. 3. Horizontal and vertical deformations were measured using LVDT as well as mechanical dial gauges placed at different locations of the beam. Strain was measured by strain gauges fixed at each face of the beam at different location as shown in Fig. 4. Harp Tendon StraightTendon Beam Edge segments Middle segments Fig. 1. Isometric view of beams and segments (a) Plan view of beam (b) Side view of beam c) End view of beam d) Shear key reinforcement e) Reinforcement of beam (Dimensions in mm) Fig. 2. Beam dimensions and reinforcement

4 Evaluation of Structural Behavior of Externally Prestressed Segmented Bridge with Shear Key under Torsion 31 Beam No. Table 1(a). Property of materials, tendon layout and load case in test beams Concrete Compressive Strength (MPa) Concrete Modulus of Elasticity (MPa) Tendon Layout Load Eccentricity (mm) 1 C Straight 0 2 C Straight 100 mm 3 C Straight 200 mm 4 D Harp 0 5 D Harp 100 mm 6 D Harp 200 mm Yield Strength and Modulus of Elasticity of reinforcement bars and prestressed tendons were 420 MPa, 200 GPa and 1700 MPa, 200 GPa respectively. Table 1(b). Property of materials, tendon layout and load case in test beams Beam Area of flat joint m 2 Area of shear key m 2 Prestressed Load kn Tendon inclination α. rad C C C D D D FRAME JACK LOAD CELL BEAM (3 SEGMENTS) SUPPORT Fig. 3. Test setup 3.4. Results Algorafi et al. (2010) presented the results of the experimental investigations of the structural behavior of EPS bridge beams under combined stresses, i.e. bending, shear and torsional stresses. The behavior of the beams was evaluated in terms of vertical deformation, twist angle, opening of segment, tendon strain, load capacity and failure mode. The structural behavior of EPS beams was significantly affected by torsion. Table 2 summarizes the part of the test results which used to propose a new equation. 4. Modification of Existing Equation to Estimate the Failure Load The existing equations in design codes are limited to estimate the failure load of externally prestressed segmented beam under combined bending moment and shear force only. The ultimate load depends on safety factors as specified by the code requirements. In the present paper, the existing equation to predict the failure load was modified by including the effect of torsion. The universally accepted theory to evaluate the shear strength of shear keys considers that the shear stresses are transmitted across the joint through two qualitatively and quantitatively different mechanisms. The first mechanism represents the friction resistance that arises when two flat and compressed surfaces attempt to slide one against the other. This resistance is proportional to the actuating compression and the corresponding proportionality factor

5 32 M. A. Algorafi, A. A. A. Ali, I. Othman, M. S. Jaafar, and R. A. Almansob is called the friction coefficient, μ1. The second mechanism considers the support effect of the castellated shear keys. These keys permit the shear transfer when there is contact between them, behaving like small plain concrete corbels. The shear strength of the keys by surface area is called cohesion, c. If compression stresses, σn, exist, then the keys turn out to be small prestressed concrete corbels, increasing the ultimate shear capacity with compression. The corresponding proportionality factor is called internal friction, μ2 (Turmo 2006). (a) Transducer arrangement (b) Typical experimental setup for test beam Fig. 4. A transducer arrangement and a typical experimental test beam set up Table 2. Summaries of deflection characteristics of all beams Beam C1 C2 C3 D1 D2 D3 Failure load (kn) * * The ultimate load of beam D1 not exist The formulae that best predicts the load carrying capacity of EPS bridges was theoretically mentioned by Turmo (2005) and Aparicio (2002) which was recommended by the AASHTO as shown in Eq. (1) below V c A A f C 1 sm n key cu 2 n (1) Where σn is average compressive stress across the joint ( MPa) Asm is area of contact between smooth surfaces in the failure plane (mm 2 ) fcu is characteristic concrete compressive strength (MPa) Akey is minimum area of the base of all shear keys in the failure plane (mm2) µ1 is the friction coefficient between concrete at the segment joint µ2 is the friction coefficient between concrete at the shear key C is the shear strength of the keys Fig. 5 shows the general case of EPS beam. The beam has shear key joint with inclined tendon and α angle. Fig. 5. General case of EPS Beam However the existing equation was improved to Eq. (2) below to consider the effect of tendon layout and the affect of combined bending moment, shear force and torsion.

6 Evaluation of Structural Behavior of Externally Prestressed Segmented Bridge with Shear Key under Torsion 33 V Where α is the tendon inclination as shown Fig. 6 N is average tendon force (kn) Eq. (2) has three terms: the first term represents the contribution of resisting shear capacity of flat joint; the second term represents the contribution of resisting shear capacity of shear key and the last term (which was modified by the author) represents the contribution of the vertical component of incline tendon resisting the downward vertical applied load. However, for beam with straight tendon layout the third term becomes zero. The result of the 6 EPS beams were used to obtain the reasonable values of the three coefficients (μ1, μ2, C) and to estimate the shear capacity of EPS beam under combined load of bending moment, shear force, normal force and torsion. The six beams have the same material and geometric property such as length, cross section reinforcement and A A f C 2N sin c (2) 1 sm n key cu 2 n tendon; however, the failure load for the beams was different. This is because of the effect of two parameters: value of torsion and tendon layout (straight and harp). Meanwhile, these parameters do not affect bending moment but affect shear. Consequently, it can be concluded that the critical failure of beams is due to shear failure of joint between segments rather than flexure failure. On the one hand, the value of shear flow for applied vertical load can be calculated. Fig. 6 shows the applied shear flow in segment joints under both shear force and torsion. Eq. (3) presents the applied shear flow for both shear force and torsion. On the other hand, Eq. (4) calculates the resisting shear flow based on Eq. (2). Then, by equating the Eqs. (3) and (4), it can obtain the reasonable values of the three coefficients (μ1, μ2, C) a) Shear flow due to shear force b) Shear flow due to torsion Fig. 6. Shear flow for shear force and torsion v v s V A sm T 0.5 Pv A sm f 0.5P e s 0.5 Pv t vs t A sm 0.5P (3a) v v t ft vt t (3b) 2Ao t 2Ao t 2Ao f R VR t (4) A Where Ao is the closed area of centreline thickness (0.2025m), t is the thickness of cross section (0.1 m). sm e νs shear stress due to shear force νt shear stress due to torsion V shear force T torsion f s f t shear flow due to shear force shear flow due to shear force e eccentricity Using nonlinear regression analysis tool of SPSS program (version 16), the best value of the three coefficients generated are μ1=0.585, μ2 = 0.453, C=0.574, with R square equal to So the resulting equation is shown below: A A f N sin Vc sm n key cu n (5)

7 34 M. A. Algorafi, A. A. A. Ali, I. Othman, M. S. Jaafar, and R. A. Almansob Table 3 summarizes the failure loads of the experimental and estimated values of failure load (Eq. (5)) for all beams. In conclusion, the proposed Eq. (5) estimates the shear capacity for EPS beam with error up to 4%. Furthermore, the correlation between the experimental and estimated values of failure load is found equal to So it is concluded that there is good correlation between the experiments and the estimated failure load. The difference is because the existing equation was limited to predicted shear capacity under shear load only. However, the proposed equation was a general equation to predict shear capacity under combined loading. Table 3: Summaries the Failure Load of beams Beam Estimated load (kn) Experimental load (kn) Difference C % C % C % D D % D % 5. Conclusion Segmental box girder bridges with external post-tensioned are one of the major new developments in bridge engineering in the last years which is a part of engineering management. In contrast to monolithic constructions, the segmental bridge consists of small precast element stressed together by external tendons. The many advantages of this type of structure include offering fast and versatile construction, no disruption at ground level, high controlled quality and cost savings that have made them the preferred solution for many long elevated highways. A series of tests were conducted to study the effect of torsion and tendon layout on the structural behavior of externally prestressed segmental concrete box beams. An existing AASHTO equation was proposed to estimate the ultimate shear capacity of EPS beam subjected to combined bending moment, shear force, normal force and torsion. This proposed equation is applicable to predict the failure of the EPS bridge when the shear failure is governed. The proposed equation predicted the ultimate shear capacity for EPS beam with error up to 4% compared to experimental value. The predicted ultimate shear capacity from the modified equation was more conservative than the predicted ultimate shear capacity from existing equation up to 16%. Acknowledgments The work conducted as part of this paper was cosponsored by the Housing Research Centre and Department of Civil Engineering, University Putra Malaysia. References Below, K. D., Hall A. S., and Rangan, B. V. (1975). Theory for concrete beams in torsion and bending. Journal of Structural Engineering, ASCE, 101, Misic, J. and Warwaruk J. (1978). Strength of prestressed solid and hollow beams subjected simultaneously to torsion, shear, and bending. ACI Structural Journal, SP55, Rabbat, B. G. and Solat K. (1987). Testing of segmental concrete girders with external tendons. Journal Prestressed Concrete Institute, 32, Ramos, G. and Aparicio, A. C (1996). Ultimate analysis of monolithic and segmental externally prestressed concrete bridges. Journal of Bridge Engineering, 1(1), Turmo J., Ramos G., and Aparicio A.C. (2005). FEM study on the structural behaviour of segmental concrete bridges with unbonded prestressing and dry joints: Simply supported bridges. Engineering Structures, 27(11), Aparicio A. C., Ramos G., and Casas J. R. (2002). Testing of externally prestressed concrete beams. Engineering Structures, 24(1), Turmo J., Ramos G., and Aparicio A. C. (2006). Shear strength of dry joints of concrete panels with and without steel fibres: Application to precast segmental bridges. Engineering Structures, 28 (1), Kordina, K., Teutsch, M., and Weber V. (1984). Spannbetonbauteile in segmentbauart under kombinierter beanspruchung aus torsion, biegung und querkraft. Journal Deutscher Ausschuss für Stahlbeton (German Committee for Structural Concrete), 350, Falkner, H., Teutsch, M., and Huang Z. (1997). Segmentbalken mit vorspannung ohne verbund unter kombinierter beanspruchung aus torsion, biegung und querkraft Journal Deutscher Ausschuss für Stahlbeton (German Committee for Structural Concrete, 472, Huang Z. and Liu X. L. (2006). Modified Skew Bending Model for Segmental Bridge with Unbonded Tendons. Journal of Bridge Engineering, 11(5), AlGorafi, M. A., Ali, A. A. A., Jaafar, M. S., and Othman I. (2007). Performance of segmental prestressed concrete bridges under combined stresses: A Critical Review. Proceeding of World Engineering Congress - CS50, Penang, Malaysia. Algorafi, M. A., Ali, A. A. A., Othman I., Jaafar, and Anwar, M. P. (2010). Experimental study of externally prestressed segmental beam under torsion, Journal of Engineering Structures. 32(11), Algorafi, M. A., (2011). The effect of torsion in externally prestressed segmental box bridge girder. PhD Thesis submitted to UPM. A.A.S.H.T.O. (1998). Guide specifications for design and construction of segmental concrete bridges. Washington.

8 Evaluation of Structural Behavior of Externally Prestressed Segmented Bridge with Shear Key under Torsion 35 Dr Mohammad A. Algorafi is a lecturer in the Civil Engineering Department, Sana a University (Yemen). His research interests in Reinforced Concrete Structures and bridge analysis. He is widely interested in non-linear analysis of structures, plastic analysis of structures, soil-structure interaction. He has been a lecturer at the many universities (SANA A (YEMEN), NOTTINGHAM (MALAYSIA CAMPUS) and KUALA LUMPUR INFRASTRUCTURE UNIVERSITY COLLEGE (MALAYSIA) since Professor Dato Abang Abdullah Abang Ali, President, Malaysian Society for Engineering & Technology (mset) and Past President, Federation of Engineering Institutions of Islamic Countries (FEIIC) and the Institution of Engineers, Malaysia (IEM) joined Universiti Putra Malaysia, as a lecturer in Structural Engineering in In 1982 he was appointed Dean, Faculty of Engineering. His research work focused on construction materials, affordable quality housing and industrialized building systems. He was promoted to the post of Professor of Civil Engineering in He was the founding Director of the Institute of Advanced Technology (ITMA) and Housing Research Centre (HRC) in the university. To date he has produced over 200 publications mainly in structural engineering and engineering education and served as editor or referee to a number of local and international journals. His research group at HRC has obtained a U.S., U.K., Swiss & Malaysian Patent and won a Geneva Innovation Gold Medal and a CIDB R&D Award for their research on an Interlocking Load bearing Hollow Block Building System. In 2002, he was elected a Fellow of the Academy of Sciences, Malaysia (ASM). Ir. Dr. Ismail Othman graduated with a B. Sc. (Civil Engineering) from UMIST, United Kingdom in He obtained his M. Sc (Advanced Structural Engineering) and Ph. D from University of Southampton, UK. He joined University Malaya as a lecturer in He was later promoted to Associate Professor in He was formerly the Head of the Civil Engineering Department, UM. He is currently the Director of University Malaya Consulting Unit (1994) and Director of UM Development and Estate Management Department. His research interests include bridge engineering, large span structures and fibre reinforced high performance concrete. He has been actively involved with the Institution of Engineers Malaysia as Chairman of Civil & Structural Technical Committee ( ) and Council Member ( ). Ramez. ALMANSOB is a full time PhD candidate in Highway Engineering in National University of Malaysia (UKM), he is doing a research under the title of, Improving the Asphalt pavement with using of nano particles, he is the secretary of Transportation Group. Dr. Mohd. Saleh Jaafar received Bachelor and Master Degrees from Michigan State University and the University of Michigan, USA, in 1985 and He obtained his PhD from the University of Sheffield, UK in He has been a lecturer at the Univeristi Pertanian Malaysia (now Universiti Putra Malaysia) since 1988 and became the Head of Civil Engineering Department in His recent achievement includes the Geneva Gold Medal award for his invention in an Interlocking Load Bearing Hollow Block System. He was appointed as Associate Professor of Civil Engineering in His area of interest includes Concrete Materials and Structural Engineering.